The intensity correlation experiment using visible light performed by Hanbury Brown & Twiss [Nature (London) (1956), 177, 27-29] is extended to X-ray wavelengths. Correlations of 14.4 keV X-ray photons from a synchrotron radiation source are observed by the coincidence counting technique. The high brilliance of synchrotron radiation available in the Tristan main ring enables the observation of two-photon correlations with a reasonable measurement time.